Research On The Path Energy Of Some Special Graphs

Graph spectrum theory is a very important research topic in algebraic graph theory.It has significant applications in network flow algorithm,molecular stability and boiling point.Based on the research of path matrix and path(signless)Laplacian matrix,this paper mainly studies the path energy of two kinds of special tricyclic graphs,the path energy and path Laplacian energy of friendship graphs and dutch windmill graphs,the path signed Laplacian energy of several simple graphs.The main content of this paper is as follows:In chapter 1,we mainly introduce the background and significance of graph theory,some related concepts of graph theory,and the research status of path matrix and path(signless)Laplacian matrix.In chapter 2,the corresponding eigenvalues of the path matrix of two kinds of special tricyclic graphs are studied by means of matrix analysis,and the path energy of these two kinds of tricyclic graphs is obtained.In chapter 3,based on the definition of path signless Laplacian matrix,the path signless Laplacian energy of graph is defined.We give the path energy and path(signless)Laplacian energy for friendship graphs and dutch windmill graphs.And the path signless Laplacian energy of several kinds of simple graphs are obtained.